Textbook Group meeting for Parr, Pezzulo, Friston 2022 .

Greetings, everyone. It is October 21st, 2022. We're in textbook group number 50.1. No, I just have a slight typo in my OBS. It's cohort two and meeting eight. We're discussing chapter four in our first discussion of chapter four. So we're going to, as we did not have any chapter or four specific questions from cohort two, today largely we're going to be reviewing and revising questions that were initially addressed in cohort one, taking a second pass and seeing where we can like add some context and simple or complex or however questions that we can add. So you can be adding in the chat or in the questions tables directly or like just unmuting and addressing them so that we can have high quality and quantity of a large diversity of questions on the material that people are curious about when they're reviewing the text. Before we go to the questions table, does anyone have any general thoughts or comments on chapter four? Yes, please, Ali. As we discussed in the previous cohort, this chapter is probably the most technical one in the whole book. So as people go through the formalism here in this chapter, I think it's quite normal to not fully understand every single equation there. So in case there are some difficulties in getting the content of this chapter, I think some of these difficulties, not all of them, would be unpacked in the later chapters. Okay. Thank you very much. Totally agreed. Anyone else want to make a general chapter four comment? Yeah, there's such an interesting rhythm. Chapter one being largely contextualizing and framing. The chapter two, three dialectic, the low road and the high road. Chapter four with a focus on the generative model, and it is a very technical chapter. Chapter five whiplashing over to neurobiology. And less on the fundamental formalisms, more on the neurobiological relationships. That constitutes the epistemic first half of the book. The second half of the book has kind of a rhyming pattern, but less focused on epistemic and more on pragmatic. Although, the pragma of epistem. Whereas chapter six is focusing more on the recipe for making the model and less of the contextualizing. Then there's another chapter pair. Seven and eight, discrete and continuous time. And then chapter nine, which is where we're heading into in just 50 minutes in the first cohort with model based data analysis. And then chapter 10 as sort of like the symmetry of chapter one and the three appendices. Okay. If anyone has comments, of course, just like raise your hand or speak up or put it in the chat or however. Okay. I'll un-upvote these so we can upvote them when we've gone through them today. Okay. Okay. Okay. Well, let's scroll through the chapter before we go to the questions, just to get a view of it. Okay. This chapter complements the preceding chapter's conceptual treatment of ACT-INF with a more formal treatment. It sets out the relationship between free energy, Bayesian inference, form of generative models, and the dynamics obtained from minimizing free energy. The key focus is on how time is represented. 4.2. Bayesian inference to free energy. 4.3. Equation 4.1 recalls Bayes' theorem. Figure 4.1 describes Jensen inequality, which is related to the tonicity of the natural log or just the logarithm function in general. And it's a pretty fundamental point. And it speaks to the advantage of using, for example, log probabilities and the different kinds of operations that are possible on logged values. Here is an application of Jensen's inequality to derive a free energy value as abounded, as abounding. Rearrangements amongst Bayes' theorem and free energy. Generative models. To calculate the free energy, we need three things. Data, a family of variational distributions, and a generative model comprising a prior and a likelihood. The section has two types of generative model. The first is dealing with categorical variables. The second deals with continuous variables. Figure 4.2 is helping gain some…